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Simplifying (2x + -9)(2x + -9) = 8 Reorder the terms: (-9 + 2x)(2x + -9) = 8 Reorder the terms: (-9 + 2x)(-9 + 2x) = 8 Multiply (-9 + 2x) * (-9 + 2x) (-9(-9 + 2x) + 2x * (-9 + 2x)) = 8 ((-9 * -9 + 2x * -9) + 2x * (-9 + 2x)) = 8 ((81 + -18x) + 2x * (-9 + 2x)) = 8 (81 + -18x + (-9 * 2x + 2x * 2x)) = 8 (81 + -18x + (-18x + 4x2)) = 8 Combine like terms: -18x + -18x = -36x (81 + -36x + 4x2) = 8 Solving 81 + -36x + 4x2 = 8 Solving for variable 'x'. Reorder the terms: 81 + -8 + -36x + 4x2 = 8 + -8 Combine like terms: 81 + -8 = 73 73 + -36x + 4x2 = 8 + -8 Combine like terms: 8 + -8 = 0 73 + -36x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 18.25 + -9x + x2 = 0 Move the constant term to the right: Add '-18.25' to each side of the equation. 18.25 + -9x + -18.25 + x2 = 0 + -18.25 Reorder the terms: 18.25 + -18.25 + -9x + x2 = 0 + -18.25 Combine like terms: 18.25 + -18.25 = 0.00 0.00 + -9x + x2 = 0 + -18.25 -9x + x2 = 0 + -18.25 Combine like terms: 0 + -18.25 = -18.25 -9x + x2 = -18.25 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = -18.25 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -18.25 + 20.25 Combine like terms: -18.25 + 20.25 = 2 20.25 + -9x + x2 = 2 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + -4.5) equal to 1.414213562 and -1.414213562.Subproblem 1
x + -4.5 = 1.414213562 Simplifying x + -4.5 = 1.414213562 Reorder the terms: -4.5 + x = 1.414213562 Solving -4.5 + x = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 1.414213562 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 1.414213562 + 4.5 x = 1.414213562 + 4.5 Combine like terms: 1.414213562 + 4.5 = 5.914213562 x = 5.914213562 Simplifying x = 5.914213562Subproblem 2
x + -4.5 = -1.414213562 Simplifying x + -4.5 = -1.414213562 Reorder the terms: -4.5 + x = -1.414213562 Solving -4.5 + x = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -1.414213562 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -1.414213562 + 4.5 x = -1.414213562 + 4.5 Combine like terms: -1.414213562 + 4.5 = 3.085786438 x = 3.085786438 Simplifying x = 3.085786438Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.914213562, 3.085786438}
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